Anthony Milford dived over in the corner three minutes later to send the 34,082 crowd into raptures but the video referee ruled the try out when Lachlan Maranta was judged to have knocked on in the build-up.
From there the Broncos struggled to get any fluency, making several handling errors in the dying stages as the Bulldogs held on for a crucial win in the context of their own finals hopes.
Broncos captain Justin Hodges was placed on report for a first half high shot on Brett Morris while Oates failed to return for the second half due to a knee injury.
The Bulldogs will also be sweating on the fitness of hooker Michael Lichaa, who jarred his knee midway through the second half and didn't return.
Celebrating his 100th match at the helm of the club, Bulldogs coach Des Hasler praised his team's ability to fight back from their early deficit.
He said despite being overrun in last weekend's defeat by the Sydney Roosters, the confidence gained from that fixture had been shown against the Broncos.
"We needed it here tonight," Hasler said.
"It was a pretty tough game of footy, I thought. Exciting right down to the last tackle.
"I was pretty pleased to see the ball grounded on that last tackle."
Hasler confirmed Lichaa is facing up to two weeks on the sidelines with his knee injury.
Broncos coach Wayne Bennett said his charges had improved on their 30-point loss to Manly last weekend but poor execution had been their undoing.
"We've won a lot of close games this year, we just happened to lose one tonight," Bennett said.
"We've lost it not because of a lack of effort or guys not turning up like we did last week in Sydney.
"We turned up tonight, just didn't have the ball control necessary to win at this level."
- AAP
